Yeah, your calculation sounds about right. But I'm not sure what the result actually means.
I'm still learning all this stuff myself, so maybe you can help me figure it out. The nozzle is a heat engine that turns the random thermal motions of the slow moving, hot, high pressure gas molecules in the combustion chamber into a cool, low pressure but rapidly moving exhaust gas. Ideally all of the heat is turned into kinetic energy and you have a rapidly moving exhaust stream at zero temperature and zero pressure.
You could do this in a vacuum with an infinitely long nozzle but that's not practical. The conversion can't be complete. As in any heat engine, some of the input heat is wasted as residual heat at a lower temperature. The exhaust is much cooler than in the combustion chamber, but still hot. So it has residual pressure, and in a vacuum the plume will immediately start to expand sideways as it leaves the nozzle, and those molecules don't contribute to thrust. Depending on why you're calculating it (e.g., to examine the effects on the lunar surface) you might want to take it into account.
The textbooks say that rocket engines produce two kinds of thrust: momentum thrust and pressure thrust. Momentum thrust is easy to understand; it's the actual exhaust velocity times the mass flow rate. Classic action-reaction. Momentum thrust is always positive, but it depends on the efficiency of the nozzle in converting heat to kinetic energy. It's generated when molecules bounce off the top of the combustion chamber, or the inside of the nozzle, transfer their momentum, and then leave without hitting any other part of the engine.
I'm still trying to grok pressure thrust. It's defined as the nozzle exit area times the difference between exhaust and ambient pressure. In an atmosphere this can be either positive or negative, but in a vacuum it's always positive. Optimum efficiency occurs when the exhaust pressure is exactly equal to ambient and pressure thrust is zero, because this maximizes both momentum thrust and overall thrust. There's an ideal nozzle length in an atmosphere. In a vacuum, a longer nozzle is always better (except for weight and size).
What bothers me is that "pressure thrust" sounds a lot like the misconception that rockets work by pushing on the air. Obviously that's not the case here, but I don't fully understand it.
It's easy to see that the random heat motions that happen to be sideways don't contribute to thrust. What I don't quite understand is the effect of those residual thermal motions that happen to be in the desired direction, i.e., parallel to the exhaust flow, but I think this is where pressure thrust comes from. I'm trying to visualize how these molecules transfer their momentum to the rocket. I think it's indirect; they bounce into each other until one eventually bounces into the engine nozzle.
What I think you've computed is yet another kind of pressure: stagnation pressure. If I understand it correctly, it's what you get when the plume impacts a large flat surface. Although the pressure in the plume may be very low (i.e., it doesn't tend to expand), when it hits the molecules will deliver their momentum in the process of being deflected sideways. Many will collide with each other and the plume will heat up as well.
